messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 4, t: 1, q: 3, a: 2}. What is the expected number of occurrences of the pattern 'q*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.64
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 1, k: 1, r: 2, z: 1, s: 5}. What is the expected number of occurrences of the pattern 'wz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 7, g: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 2, e: 5, y: 3}, what is the expected number of times the pattern 'y+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 2, a: 1, n: 2, v: 1, g: 4}. What is the expected number of occurrences of the pattern 'a+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.18
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, n: 2, e: 1, c: 3, b: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, g: 4, k: 3, h: 1}, what is the expected number of times the pattern 'hg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.74
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 1, y: 2, s: 2, o: 4, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 5, q: 5} to form a word, what is the expected number of matches of the pattern 'xq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 3, c: 5, g: 2}. What is the expected number of occurrences of the pattern 'co*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.3
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, g: 3, d: 3}, what is the expected number of times the pattern 'gj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.71
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 2, y: 2, z: 6}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, j: 3, c: 4}, what is the expected number of times the pattern 'c+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.71
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, p: 5}, what is the expected number of times the pattern 'pn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 7, v: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {s: 2, d: 2, e: 6}, what is the expected number of times the pattern 'se*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.9
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, q: 4, f: 3}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 1, t: 2, y: 4, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 4, y: 1, a: 3, d: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 4, k: 5, g: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 2, e: 1, k: 3, h: 4}, what is the expected number of times the pattern 'm+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, t: 1, p: 1, s: 3}, what is the expected number of times the pattern 'tp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.54
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {f: 2, c: 3, z: 3, j: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 2, a: 3, v: 2, t: 2, q: 1}. What is the expected number of occurrences of the pattern 'a+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 7, t: 3}, what is the expected number of times the pattern 'tc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 2, x: 4, n: 2, k: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 3, l: 4, w: 3} to form a word, what is the expected number of matches of the pattern 'lo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.64
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {x: 5, d: 5} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 5, n: 3, e: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 3, z: 7} to form a word, what is the expected number of matches of the pattern 'z.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 1, l: 4, q: 2, i: 3}, what is the expected number of times the pattern 'ol*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.74
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 7, x: 3}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 3, s: 4, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 2, t: 5, b: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'k*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 6, k: 4}, what is the expected number of times the pattern 'ok*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 2, w: 4, c: 4} to form a word, what is the expected number of matches of the pattern 'j*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 3, j: 5, m: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, j: 2, s: 2, e: 3, k: 1}. What is the expected number of occurrences of the pattern 'ej+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.29
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 5, a: 5}, what is the expected number of times the pattern 'ga*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 2, k: 3, p: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 2, n: 4, h: 1, d: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 3, x: 2, c: 4, k: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, j: 4}, what is the expected number of times the pattern 'd*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 1, c: 6, w: 3}. What is the expected number of occurrences of the pattern 'wc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.35
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 6, s: 4}. What is the expected number of occurrences of the pattern 'n+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 4, r: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'dr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.64
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 1, j: 1, z: 5, y: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.72
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 2, c: 2, x: 1, o: 4, s: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 3, k: 2, m: 3, w: 2} to form a word, what is the expected number of matches of the pattern 'w+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.19
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 5, d: 5}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {u: 1, p: 4, o: 3, f: 2} to form a word, what is the expected number of matches of the pattern 'up+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.24
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 3, n: 3, e: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'n*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 4, m: 1, v: 2, n: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 2, c: 1, x: 2, y: 1, v: 4}. What is the expected number of occurrences of the pattern 'v*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 3, k: 4, r: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 2, l: 2, p: 1, i: 3, t: 2}. What is the expected number of occurrences of the pattern 'i*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.66
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, o: 3, m: 3, l: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, z: 3, u: 2, x: 1, o: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 1, n: 3, w: 4, s: 2}. What is the expected number of occurrences of the pattern 'l.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.44
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 2, s: 4, t: 3, l: 1} to form a word, what is the expected number of matches of the pattern 's+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.24
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 6, d: 4} to form a word, what is the expected number of matches of the pattern 'd+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 1, a: 5, x: 4} to form a word, what is the expected number of matches of the pattern 'e.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.56
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 2, c: 2, e: 1, n: 2, g: 3}, what is the expected number of times the pattern 'l.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 2, o: 4, v: 2, e: 2}, what is the expected number of times the pattern 'ho+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 4, f: 6}. What is the expected number of occurrences of the pattern 'k*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.43
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, i: 9}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 4, m: 1, o: 3, p: 1, j: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 3, o: 4, r: 3}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 2, r: 2, e: 5, b: 1} to form a word, what is the expected number of matches of the pattern 'd+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 7, u: 3} to form a word, what is the expected number of matches of the pattern 'mu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.63
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 2, r: 1, h: 3, u: 4} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 2, r: 3, l: 3, i: 2}. What is the expected number of occurrences of the pattern 'ri*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 5, i: 5} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {x: 4, b: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 3, q: 4, c: 3}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 2, p: 3, o: 2, r: 2, t: 1}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 5, b: 5} to form a word, what is the expected number of matches of the pattern 'h.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.78
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 1, u: 4, n: 2, a: 3}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, p: 1, v: 6, w: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {z: 3, k: 2, r: 1, c: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'rc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.66
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {o: 1, a: 2, p: 3, t: 1, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, g: 7}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 2, o: 3, d: 2, b: 3} to form a word, what is the expected number of matches of the pattern 'o+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 2, q: 2, j: 2, a: 3, f: 1}. What is the expected number of occurrences of the pattern 'a.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {r: 1, t: 3, l: 2, a: 3, x: 1}. What is the expected number of occurrences of the pattern 'r.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 5, r: 5}. What is the expected number of occurrences of the pattern 'dr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, z: 3, d: 2, o: 2}, what is the expected number of times the pattern 'o*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 2, y: 4, d: 2, k: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 6, p: 4} to form a word, what is the expected number of matches of the pattern 'w*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, m: 3, g: 1, h: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 5, g: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 1, a: 3, g: 2, w: 4}, what is the expected number of times the pattern 'wa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.64
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, z: 3, p: 5}, what is the expected number of times the pattern 'p*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 3, c: 3, o: 4} to form a word, what is the expected number of matches of the pattern 'k*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.64
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 2, p: 1, m: 4, k: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'm+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 5, k: 5}, what is the expected number of times the pattern 'y.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.78
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 4, e: 6}. What is the expected number of occurrences of the pattern 'w+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, s: 8}, what is the expected number of times the pattern 'c*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.78
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 3, s: 4, q: 3} to form a word, what is the expected number of matches of the pattern 'd+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 1, v: 2, q: 2, r: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
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